Spots and the Activity of Stars in the Hyades Cluster from Observations with the Kepler Space Telescope (K2)

Observations of the K2 mission (continuing the program of the Kepler Space Telescope) are used to estimate the spot coverage S (the fractional area of spots on the surface of an active star) for stars of the Hyades cluster. The analysis is based on data on the photometric variations of 47 confirmed single cluster members, together with their atmospheric parameters, masses, and rotation periods. The resulting values of S for these Hyades objects are lower than those stars of the Pleiades cluster (on average, by ΔS ~ 0.05?0.06). A comparison of the results of studies of cool, low-mass dwarfs in the Hyades and Pleiades clusters, as well as the results of a study of 1570 M stars from the main field observed in the Kepler SpaceMission, indicates that the Hyades stars are more evolved than the Pleiades stars, and demonstrate lower activity. The activity of seven solar-type Hyades stars (S = 0.013 ± 0.006) almost approaches the activity level of the present-day Sun, and is lower than the activity of solar-mass stars in the Pleiades (S = 0.031 ± 0.003). Solar-type stars in the Hyades rotate faster than the Sun (〈P〉 = 8.6 ^d ), but slower than similar Pleiades stars.     

The Spots and Activity of Stars in the Beehive Cluster Observed by the Kepler Space Telescope (K2)

The spottedness parameters S (the fraction of the visible surface of the star occupied by spots) characterizing the activity of 674 stars in the Beehive Cluster (age 650 Myr) are estimated, together with variations of this parameter as a function of the rotation period, Rossby number Ro and other characteristics of the stars. The activity of the stars in this cluster is lower than the activity of stars in the younger Pleiades (125 Myr). The average S value for the Beehive Cluster stars is 0.014, while Pleiades stars have the much higher average value 0.052. The activity parameters of 61 solar-type stars in the Beehive Cluster, similar Hyades stars (of about the same age), and stars in the younger Pleiades are compared. The average S value of such objects in the Beehive Cluster is 0.014± 0.008, nearly coincident with the estimate obtained for solar-type Hyades stars. The rotation periods of these objects are 9.1 ± 3.4 day, on average, in agreement with the average rotation period of the Hyades stars (8.6 ^d ). Stars with periods exceeding 3–4 ^d are more numerous in the Beehive Cluster than in the Pleiades, and their periods have a larger range, 3–30 ^d . The characteristic dependence with a kink at Ro (saturation) = 0.13 is not observed in the S–Rossby number diagram for the Beehive and Hyades stars, only a clump of objects with Rossby numbers Ro > 0.7. The spottedness data for the Beehive Cluster and Hyades stars are in good agreement with the S values for dwarfs with ages of 600–700 Myr. This provides evidence for the reliability of the results of gyrochronological calibrations. The data for the Beehive and Pleiades stars are used to analyze variations in the spot-forming activity for a large number of stars of the same age that are members of a single cluster. A joint consideration of the data for two clusters can be used to draw conclusions about the time evolution of the activity of stars of different masses (over a time interval of the order of 500 Myr).     

Spots and activity of solar-type stars from Kepler observations

The spot coverages S for 2846 solar-type stars with effective temperatures from 5700 K to 5800 K and gravities from 4.4 to 4.5 have been measured. An analysis based on the MAST catalog, which presents photometric measurements obtained with the Kepler Space Telescope during Q9 is presented. The existence of two groups of solar-type stars, with S values between 0.001 and 0.007 and with S > 0.007, is inferred. The second group (active stars) contains 279 stars (about 10% of the total number of stars analyzed). The mean S parameter for the entire sample is 0.004, comparable to the mean spot coverage of the Sun. In general, the dependence of S on the rotation period for solar-type stars has characteristics similar to those found earlier for stars with exoplanets. For the vast majority of the stars in the sample, the activity is constant, and independent of age. The activity of the small number of active stars with S > 0.007 decreases with age. The age variations of the chromospheric activity index R′_HK are compared to variations of the spot coverage S. The relations analyzed have common characteristic features. It is likely that both the spot activity level and the chromospheric activity level abruptly decrease for stars older than 4 billion yrs.     

Analysis of magnetic activity of the rapidly rotating stars He 373 and AP 225

Spectroscopic and photometric data for the two rapidly rotating members of the α Persei cluster He 373 and AP 225 are analyzed. Improved estimates have been obtained for the projected equatorial rotation velocities: v sin i = 164 km/s for He 323 and v sin i = 129 km/s for AP 225. Multi-band photometric mapping is used to map the spot distributions on the surfaces of the two stars. The fractional spotted areas S and mean temperature difference ΔT between the unspotted photosphere and the spots are estimated (S = 7% and ΔT = 1000 K for He 373; S = 9% and ΔT = 800 K for AP 225). The H _α line profiles of both stars have variable emission components whose widths are used to deduce the presence of extended regions of emission reaching the corotation radius.     

Long-term Spot-Coverage Variations of 13 BY Dra G–K Dwarfs

The results of spot-coverage modeling for 13 active G–K dwarf stars based on many-year photometric observations are presented. The results of UBVRI observations of eight stars performed at the Crimean Astrophysical Observatory were used together with data from the literature in this analysis. The spot-coverage parameters for 13 selected BY Dra active red dwarfs have been redetermined to improve the zonal spot-coverage model for the stellar photospheres, which currently allows for the presence of two active longitudes. Time variations of the spot-activity characteristics of these systems were analyzed with the aim of searching for possible cyclic variations. All the stars, with the exception of OU Gem and BE Cet, show fairly strong correlations between variations in the spot latitudes and spot areas, with absolute values of the correlation coefficients, R(〈?〉, S), ranging from 0.38 to 0.92. For five stars, an anti-correlation between the mean latitude and area of the spots was found (R(〈?〉, S) from–0.24 to–0.73). This behavior may reflect the drift of spots toward the equator in the course of their development. Eight stars feature positive correlations, i.e. the spots drift towards the pole as their areas increase. Nine stars demonstrate activity cycles, which are reflected in photometric variations as well as variations of the spot areas and mean latitudes. The periods of the latitude drift of the spots are found for five stars; the magnitudes of the spot-latitude drift rates are lower than the corresponding value for sunspots by a factor of 1.5–3.     

A model for the population of helium stars in the Galaxy: Low-mass stars

We model the Galactic ensemble of helium stars using population synthesis techniques, assuming that all helium stars are formed in binaries. In this picture, single helium stars are produced by mergers of helium remnants of the components of close binaries (mainly, the merging of helium white dwarfs) or in the disruption of binaries with helium components during supernova explosions. The estimated total birthrate of helium stars in the Galaxy is 0.043 yr^?1; the total number is 4 × 10⁶; and the binarity rate is 76%. We construct a subsample of low-mass (M_He ? 2M_⊙) helium stars defined by observational selection effects: the limiting magnitude (V_He ≤ 16), ratio of the magnitudes of the components in binaries (V_He ≤ V_comp), and lower limit for the semiamplitude of the radial velocity required for detecting binarity (K_min = 30 km s^?1). The parameters of this subsample are in satisfactory agreement with observations of helium subdwarfs. In particular, the binarity rate in the selection-limited sample is 58%. We analyze the relations between the orbital periods and masses of helium subdwarfs and their companions in systems with various combinations of components. We predict that the overwhelming majority (～97%) of unobserved companions to helium stars will be white dwarfs, predominantly, carbon-oxygen white dwarfs.     

Analysis of the velocity field of F and G dwarfs in the solar neighborhood as a function of age

The space velocities from the catalog of Nordstr?m et al. (2004) are used to trace variations of a number of kinematic parameters of single F and G dwarfs as a function of their age. The vertex deviation of disk stars increases from 7° ± 1° to 15° ± 2° as the mean age decreases from 4.3 to 1.5 Gyr. The two-dimensional velocity distributions in the UV, UW, and VW planes are analyzed. The evolution of the main peaks in the velocity distributions can be followed to an average age of ≈9 Gyr. We find that: (1) in the distributions of the UV velocity components, stars of different types are concentrated toward several stable peaks (the Hyades, Pleiades, and Sirius Cluster), suggesting that the stars belonging to these formations did not form simultaneously; (2) the peak associated with the Hyades Cluster dominates in all age intervals; and (3) the Hyades peak is strongest for stars with an average age of 1.5 Gyr, suggesting that this peak contains a considerable fraction of stars from the Hyades cluster. The age dependences of the kinematic parameters exhibit a break near ≈4–5 Gyr, which can be explained as an effect of the different contributions of stars of the thin and thick disks. The Stromberg relation yields a solar LSR velocity of V _⊙LSR = (8.7, 6.2, 7.2) ± (0.5, 2.2, 0.8) km/s.     

Logarithmic density range and the percentage of stars in the cores of various subsystems of the globular clusters M56, M12, NGC 6535, NGC 6171, NGC 5466, and M92

Lower limits for the percentages of stars with various luminosities in the cores of six globular clusters are derived using stellar spatial density distributions f(r) to deep limiting B magnitudes obtained earlier. For NGC 6535 and NGC 5466, the logarithmic density range and Kholopov parameters D_f and D_r are also determined. These two parameters are correlated with the mean masses of stars of various subsystems and the total mass (number) of stars in the cluster.     

Spots and the activity of M dwarfs from observations with the Kepler Space Telescope

A method for estimating the spottedness parameter S (the spotted area as a fraction of the surface of an active star) proposed earlier is applied to an analysis of activity in 1570 M dwarf stars. The analysis is based on observational material obtained with the Kepler Space Telescope, as well as data on the fluxes of the studied objects in the near and far ultraviolet (NUV and FUV) based on data from the GALEX space telescope. The variations of S with the ages of the stars are studied (four groups with different ages are distinguished), as well as variations of S with their rotational periods. A diagram characterizing the relationship between S and the Rossby number Ro resembles the classical dependence of the X-ray luminosities of active stars on Ro, and a saturation regime is attained at the same value, Ro = 0.13. Moreover, objects with ages of more than 100 million years do not form a single sequence (and stars older than 900 million years possess surface spottednesses of order 1%). The S?Ro dependence obtained could expand possibilities for analyzing the dependence of the X-ray luminosities of active stars on their Rossby numbers, and could also be applied to refine parameters characterizing the action of dynamo mechanisms, such as the dynamo number N _D . A comparison of the GALEX NUV and FUV brightness estimates with the activity parameters of the stars suggests that younger, more rapidly rotating active stars are brighter in the NUV, and that the FUV flux grows and the difference of the FUV and NUV brightnesses decreases with increasing spottedness S.     

The evolutionary status of ultraluminous X-ray sources

We analyze models for quasi-stationary, ultraluminous X-ray sources (ULXs) with luminosities 10³⁸–10⁴⁰ erg/s exceeding the Eddington limit for a ～1.4M_⊙ neutron star. With the exception of relatively rare stationary ULXs that are associated with supernova remnants or background quasars, most ULXs are close binary systems containing a massive stellar black hole (BH) that accretes matter donated by a stellar companion. To explain the observed luminosities of ～10⁴⁰ erg/s, the mass of the BH must be ～40M_⊙ if the accreted matter is helium and ～60M_⊙ if the accreted matter has the solar chemical composition. We consider donors in the form of main-sequence stars, red giants, red supergiants, degenerate helium dwarfs, heavy disks that are the remnants of disrupted degenerate dwarfs, helium nondegenerate stars, and Wolf-Rayet stars. The most common ULXs in galaxies with active star formation are BHs with Roche-lobe-filling main-sequence companions with masses ～7M_⊙ or close Wolf-Rayet companions, which support the required mass-exchange rate via their strong stellar winds. The most probable candidate ULXs in old galaxies are BHs surrounded by massive disks and close binaries containing a BH and degenerate helium-dwarf, red-giant, or red-supergiant donor.     

The impact of reflection effects on the parameters of the old pre-cataclysmic variables MS Peg and LM Com

We have determined the main parameters of the old precataclysmic variable stars MS Peg and LM Com. The radial velocities of the components, reflection effects in the spectra, and light curves of the systems are studied based on model stellar atmospheres subject to external irradiation. Forty-seven moderate-resolution spectra for MS Peg and 57 for LM Com obtained with the 6-m telescope of the Special Astrophysical Observatory are used to derive the refined orbital periods of 0.1736660 days and 0.2586873 days, respectively; the orbital eccentricities do not exceed e=0.04. The mass (M _w =0.49e_⊙) and radius (e _w =0.015R_⊙) of the MS Peg primary calculated using the gravitational redshift correspond to those for a cooling carbon white dwarf with a thin hydrogen envelope. The parameters of the red dwarf (M _r =0.19M_⊙, T_eff=3560 K, R _r =0.18R_⊙) are close to those derived from evolutionary tracks for main-sequence M stars with solar chemical composition. The radius (R _r =0.22R_⊙) and temperature (T_eff=3650 K) of the LM Com secondary exceed theoretical estimates for main-sequence stars with masses of M _r =0.17M_⊙. The luminosity excess of the red dwarf in LM Com can be explained by a prolonged (T>5×10⁶ yrs) relaxation of the M star to its normal state after the binary leaves the common-envelope stage. For both systems, theoretical U, B, V, and R light curves and spectra calculated using the adopted sets of parameters are generally consistent with the observations. This confirms the radiative origin of the hot spots, the unimportance of horizontal radiative transport, and the absence of large-scale velocity fields with high values (V_trans>50 km/s) at the surfaces of the secondaries. Most of the emission lines in the spectra of these objects are formed under conditions close to thermalization, enabling modeling of their pro files in an LTE approximation. A strong λ3905 Å emission line has been identified as the 3s²3p4s 1P⁰-3s²3p² 1S SiI λ3905.52 Å line formed in the atmosphere of the hot spot. The observed intensity can be explained by non-LTE “superionization” of SiI atoms by soft UV radiation from the white dwarf. We suggest a technique for identifying binaries whose cool components are subject to UV irradiation based on observations of λ3905 Å emission in their spectra.     

Evolution of close binaries and gamma-ray bursts

We analyze the late stages of evolution of massive (M ₀ ? 8 M _⊙) close binaries, from the point of view of possible mechanisms for the generation of gamma-ray bursts. It is assumed that a gamma-ray burst requires the formation of a massive (～1 M _⊙), compact (R ? 10 km) accretion disk around a Kerr black hole or neutron star. Such Kerr black holes are produced by core collapses of Wolf-Rayet stars in very close binaries, as well as by mergers of neutron stars and black holes or two neutron stars in binaries. The required accretion disks can also form around neutron stars that were formed via the collapse of ONeMg white dwarfs. We estimate the Galactic rate of events resulting in the formation of rapidly rotating relativistic objects. The computations were carried out using the “Scenario Machine.”     

Wolf-Rayet stars,black holes,and gamma-ray bursters in close binaries

We consider the evolutionary status of observed close binary systems containing black holes and Wolf-Rayet (WR) stars. When the component masses and the orbital period of a system are known, the reason for the formation of a WR star in an initial massive system of two main-sequence stars can be established. Such WR stars can form due to the action of the stellar wind from a massive OB star (M_OB≥50M_⊙), conservative mass transfer between components with close initial masses, or the loss of the common envelope in a system with a large (up to ～25) initial component mass ratio. The strong impact of observational selection effects on the creation of samples of close binaries with black holes and WR stars is demonstrated. We estimate theoretical mass-loss rates for WR stars, which are essential for our understanding the observed ratio of the numbers of carbon and nitrogen WR stars in the Galaxy \(\dot M_{WR} (M_ \odot yr^{ - 1} ) = 5 \times 10^{ - 7} (M_{WR} /M_ \odot )^{1.3} \). We also estimate the minimum initial masses of the components in close binaries producing black holes and WR stars to be ～25M_⊙. The spatial velocities of systems with black holes indicate that, during the formation of a black hole from a WR star, the mass loss reaches at least several solar masses. The rate of formation of rapidly rotating Kerr black holes in close binaries in the Galaxy is ～3×10^?6 yr^?1. Their formation may be accompanied by a burst of gamma radiation, possibly providing clues to the nature of gamma-ray bursts. The initial distribution of the component mass ratios for close binaries is dN～dq=dM₂/M₁ in the interval 0.04?q₀≤1, suggesting a single mechanism for their formation.     

Is NGC 7006 a globular cluster with a primarily red horizontal branch?

A CCD BV R photometric study of the central region (15″ ≤ r ≤ 100″) of the globular cluster NGC 7006 based on color-magnitude diagrams is presented. We find for the main parameters of the cluster [Fe/H] = ?1.62, Y = 0.21, E _B?V = 0.15 ^m , V _HB = 18.84 ^m , M _V ^HB =+0.56 ^m , R _⊙ = 37.1 kpc). Two previously unknown RR Lyr variables were discovered in the central region of the cluster. The morphological index of the horizontal branch for the entire region studied indicates that the red stellar population dominates, consistent with previous studies: HB _mi = ?0.13. Such anomalously negative morphological indices are possessed by a whole group of Ool clusters with intermediate metallicities, which also display a characteristic distribution of stars along the horizontal branch. There is a radial dependence for the horizontal-branch morphology, with the color becoming primarily blue with approach toward the cluster center. One possible origin for this behavior could be the effect of inner dynamical processes on the spatial distribution of hot stars.     

Estimation of the accuracy of methods for determining component masses for low-mass X-ray binary systems

Modern modeling of the population of low-mass X-ray binary systems containing black holes applying standard assumptions leads to a lack of agreement between the modeled and observed mass distributions for the optical components, with the observed masses being lower. This makes the task of estimating the systematic errors in the derived component masses due to imperfect models relevant. To estimate the influence of systematic errors in the derived masses of stars in X-ray binary systems, we considered two approximations for the tidally deformed star in a Roche model. Approximating the star as a sphere with a volume equal to that of the Roche lobe leads to slight overestimation of the equatorial rotational velocity V _rot sin i, and hence to slight underestimation of the mass ratio q = M _x /M _v . Approximating the star as a flat, circular disk with constant local line profiles and a linear limb-darkening law (a classical rotational broadeningmodel) is an appreciably cruder approach, and leads to overestimation of V _rot sin i by about 20%. In the case of high values of q = M _x /M _v , this approximation leads to substantial underestimation of the mass ratio q, which can reach several tens of percent. The mass of the optical star is overestimated by a factor of 1.5 in this case, while the mass of the black hole is changed only slightly. Since most estimates of component mass ratios for X-ray binary systems are carried out using a classical rotational broadening model for the lines, this leads to the need for appreciable corrections to (reductions of) previously published masses for the optical stars, which enhances the contradiction with the standard evolutionary scenario for low-mass X-ray binaries containing black holes.     

Evolution of the masses of neutron stars in binary systems

We study the growth of the masses of neutron stars in binary systems due to the accumulation of mass from the optical donors accreted onto the neutron-star surface. Possible scenarios for this accretion are considered. The masses and magnetic-field strengths of radio pulsars derived using population-synthesis methods are compared to the observational data. The population-synthesis analysis indicates that a neutron star can increase its mass from the standard value of m _x ? 1.35M_⊙ to the Oppenheimer-Volkoff limit, m _x ? 2.5M_⊙, via accretion from a companion.     

Late stages of the evolution of close compact binaries: Type I supernovae,gamma-ray bursts,and supersoft X-ray sources

We consider the evolution of close binaries resulting in the most intensive explosive phenomena in the stellar Universe—Type Ia supernovae and gamma-ray bursts. For Type Ia supernovae, which represent thermonuclear explosions of carbon-oxygen dwarfs whose masses reach the Chandrasekhar limit during the accretion of matter from the donor star, we derive the conditions for the accumulation of the limiting mass by the degenerate dwarf in the close binary. Accretion onto the degenerate dwarf can be accompanied by supersoft X-ray radiation with luminosity 1–10⁴ L _⊙. Gamma-ray bursts are believe to accompany the formation and rapid evolution of compact accretion-decretion disks during the formation of relativistic objects—black holes and neutron stars. The rapid (～1 M _⊙/s) accretion of matter from these disks onto the central compact relativistic star results in an energy release of ～0.1 M _⊙ c ² ～ 10⁵³ erg in the form of gamma-rays and neutrinos over a time of 0.1–1000 s. Such disks can form via the collapse of the rapidly rotating cores of Type Ib, Ic supernovae, which are components in extremely close binaries, or alternately due to the collapse of accreting oxygen-neon degenerate dwarfs with the Chandrasekhar mass into neutron stars, or the merging of neutron stars with neutron stars or black holes in close binaries. We present numerical models of the evolution of some close binaries that result in Type Ia supernovae, and also estimate the rates of these supernovae (～0.003/year) and of gamma-ray bursts (～10^?4/year) in our Galaxy for various evolutionary scenarios. The collimation of the gamma-ray burst radiation within an opening angle of several degrees “matches” the latter estimate with the observed rate of these events, ～10^?7–10^?8/year calculated for a galaxy with the mass of our Galaxy.     

Activity of Young Dwarfs with Planetary Systems: EPIC 211901114 and K2–33

The results of an analysis of the activity of the young stars with planetary systems EPIC 211901114 and K2–33 based on observational data obtained over 70 days with the Kepler Space Telescope are presented. The rotation periods of EPIC 211901114 (8.56±0.60^d) and K2–33 (6.29±0.50^d) have been found. Maps of temperature inhomogeneities on the surfaces of EPIC 211901114 and K2–33 have been constructed. No relative displacements of the active regions on the stellar surface have been foundfor EPIC 211901114. The differential-rotation parameter has been estimated for K2–33, ΔΩ = 0.0039±(0.0020–0.0012) rad/day. The fractional spotted area S on the surface of EPIC 211901114 reaches about 5% of its total visible surface. For K2–33, S is 3.8% of its total visible surface, on average. On the whole, the positions of EPIC 211901114 and K2–33 on S–age, S–rotation period, and S–Rossby number diagrams match the general character of the dependence found earlier for M dwarfs. The flare activity of EPIC 211901114 and K2–33 has been studied, based on 32 flares of EPIC 211901114 and 7 flares of K2–33. The flare frequencies and amplitudes for EPIC 211901114 and K2–33 have been estimated, together with the time scales for their rise and decay. The flare energies have also been estimated, 10^32.1?33.4 and 10^32.2?33.3 erg for EPIC 211901114 and K2–33, respectively.     

Comparison of the magnetic properties of leading and following spots and the overlying ultraviolet emission

SDO/HMI and SDO/AIA data for the 24th solar-activity cycle are analyzed using a quicker and more accurate method for resolving π ambiguities in the transverse component of the photospheric magnetic field, yielding new results and confirming some earlier results on the magnetic properties of leading and following magnetically connected spots and single spots. The minimum inclination of the field lines to the positive normal to the solar surface α _min within umbrae is smaller in leading than in following spots in 78% of the spot pairs considered; the same trend is found for the mean angle 〈α〉 in 83% of the spot pairs. Positive correlations between the α _min values and the 〈α〉 values in leading and following spots are also found. On average, in umbrae, the mean values of 〈B〉, the umbra area S, and the angles α _min and 〈α〉 decrease with growth in the maximum magnetic field B _max in both leading and following spots. The presence of a positive correlation between B _max and S is confirmed, and a positive correlation between 〈B〉 and S in leading and following spots has been found. Themagnetic properties of the umbrae of magnetically connected pairs of spots are compared with the contrast of the He II 304 emission above the umbrae, C ₃₀₄. Spots satisfying certain conditions display a positive correlation between C _304?L and 〈α _L 〉 for the leading (L) spots, and between C _304?L /C _304?F and l _L /l _F , where l _L (l _F ) are the lengths of the field lines connecting leading (L) or following (F) spots from the corresponding spot umbrae to the apex of the field line.     

IR photometry and models for the dust envelopes of two carbon stars

The results of JHKLM photometry of two carbon stars are presented: the irregular variable NQ Cas and the Mira star BD Vul. Data on the mean fluxes supplemented with mid-IR observations with the IRAS, AKARI, andWISE satellites are used to compute spherically symmetrical model dust envelopes for the stars, consisting of particles of amorphous carbon and silicon carbide. The optical depth in the visible for the comparatively cool dust envelope of BD Vul, with a dust temperature at its inner boundary T₁ = 610 K, is fairly low: τ_V = 0.13. The dust envelope of NQ Cas is appreciably hotter (T₁ = 1550 K), and has τ_V = 0.32. The estimated mass-loss rates are 1.5 × 10^?7M_⊙/yr for NQ Cas and 5.9 × 10^?7M_⊙/yr for BD Vul.